QJEEAdv15Phc115: JEE Advanced 2015 Physics - Class 12 JEEAdv15Phc115 Solution: An electron in an excited state of Li 2+ ion has angular…

Question

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An electron in an excited state of Li²⁺ ion has angular momentum

\frac{3 h}{2 π}

. The de Broglie wavelength of the electron in this state is p

π

a₀ (where a₀ is the Bohr radius). The value of p is

Accepted Answer

Angular momentum $m v r = \frac{n h}{2 π}$ where $r = 3 a_{0}$ where $n = 3$ , that is, electron in $L i^{2 +}$ is in second excited state

$λ = \frac{h}{m v} = p π a_{0}$

$\Rightarrow n = p π (m v a_{0}) = p π (\frac{m v r}{3}) = \frac{p π}{3} (\frac{3 h}{2 π}) = \frac{p h}{2}$

Therefore, $p = 2$ .

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